Let's solve the problem step by step, with explanations for each step. --- ## **Step 1: Understanding the Problem** We have: - Two glass layers, each **6.5 mm** thick - Air gap between glass layers: **6 mm** - **Thermal conductivity (k)**: - Glass: **0.869 W/m·K** - Air: **0.026 W/m·K** - **Temperature difference (\(\Delta T\))**: **31 K** - **Window dimensions**: **1.0 m × 2.0 m** We are to **calculate the total heat loss (Q) through the window**. --- ## **Step 2: Calculate Thermal Resistances** For heat transfer through a flat wall (or window), **thermal resistance \( R \) is:** \[ R = \frac{L}{kA} \] Where: - \( L \) = thickness (m) - \( k \) = thermal conductivity (W/m·K) - \( A \) = area (m²) **Glass Layer:** - Thickness = 6.5 mm = 0.0065 m - \( k_{glass} = 0.869 \) W/m·K **Air Layer:** - Thickness = 6 mm = 0.006 m - \( k_{air} = 0.026 \) W/m·K **Window Area:** \[ A = 1.0 \times 2.0 = 2.0 \text{ m}^2 \] Now, calculate the resistance for each layer: ### **a) Resistance of One Glass Layer** \[ R_{glass} = \frac{L_{glass}}{k_{glass} \cdot A} = \frac{0.0065}{0.869 \times 2} \] \[ R_{glass} = \frac{0.0065}{1.738} \approx 0.00374 \text{ K/W} \] ### **b) Resistance of Air Layer** \[ R_{air} = \frac{L_{air}}{k_{air} \cdot A} = \frac{0.006}{0.026 \times 2} \] \[ R_{air} = \frac{0.006}{0.052} \approx 0.1154 \text{ K/W} \] --- ## **Step 3: Total Thermal Resistance** Since the layers are **in series**, total resistance is the sum: \[ R_{total} = R_{glass1} + R_{air} + R_{glass2} \] \[ R_{total} = 0.00374 + 0.1154 + 0.00374 = 0.12288 \text{ K/W} \] --- ## **Step 4: Calculate Heat Loss** The heat loss rate \( Q \) is given by: \[ Q = \frac{\Delta T}{R_{total}} \] \[ Q = \frac{31}{0.12288} \approx 252.25 \text{ W} \] --- ## **Step 5: Final Answer** ### **The heat loss through the window is:** \[ \boxed{252 \text{ W}} \] --- ### **Summary Table of Resistances** | Layer | Resistance (K/W) | |---------------|------------------| | Glass (1) | 0.00374 | | Air | 0.1154 | | Glass (2) | 0.00374 | | **Total** | **0.12288** | --- **Explanation:** The heat transfer is limited mainly by the air gap, which has much higher resistance than the glass. The total resistance allows you to use the temperature difference to find the heat loss using Ohm's Law analogy for heat transfer.